Unconventional scaling theory in disorder-driven quantum phase transition

TL;DR

This paper investigates unique scaling behaviors of conductance and localization length in a disorder-driven quantum phase transition between band insulator and Weyl semimetal phases, revealing anisotropic scale invariance.

Contribution

It introduces novel scaling functions for conductance and localization length, supported by transfer-matrix calculations, highlighting anisotropic scale invariance at the critical point.

Findings

Unconventional scaling functions are verified numerically.

Anisotropic scale invariance governs the quantum criticality.

Critical conductance distribution exhibits novel behavior.

Abstract

We clarify novel forms of scaling functions of conductance, critical conductance distribution and localization length in a disorder-driven quantum phase transition between band insulator and Weyl semimetal phases. Quantum criticality of the phase transition is controlled by a clean-limit fixed point with spatially anisotropic scale invariance. We argue that the anisotropic scale invariance is reflected on unconventional scaling function forms in the quantum phase transition. We verify the proposed scaling function forms in terms of transfer-matrix calculations of conductance and localization length in a tight-binding model.